Pith Number

pith:BRMFWFR4

pith:2007:BRMFWFR47BYLJYCUOIRGXQBQPT

not attested not anchored not stored refs pending

Group actions on algebraic stacks via butterflies

Behrang Noohi

arxiv:0704.1010 v2 · 2007-04-08 · math.AG · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BRMFWFR47BYLJYCUOIRGXQBQPT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:14:08.970514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c585b163cf870b4e05472226bc0307cc91a12b3f081bb110d349cd039a594fe

Aliases

arxiv: 0704.1010 · arxiv_version: 0704.1010v2 · doi: 10.48550/arxiv.0704.1010 · pith_short_12: BRMFWFR47BYL · pith_short_16: BRMFWFR47BYLJYCU · pith_short_8: BRMFWFR4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BRMFWFR47BYLJYCUOIRGXQBQPT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0c585b163cf870b4e05472226bc0307cc91a12b3f081bb110d349cd039a594fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a1ef7b2ba681388c9c6df709e963d4f8b5cf18516dfb937567244ddfdd46682",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-04-08T03:26:16Z",
    "title_canon_sha256": "affa0221965b01e3e4091314dd575a46b23a9e048d5b38018a824273f18afb5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0704.1010",
    "kind": "arxiv",
    "version": 2
  }
}